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CAML: Commutative Algebra Machine Learning─A Case Study on Protein–Ligand Binding Affinity Prediction
Recently, Suwayyid and Wei introduced commutative algebra as an emerging paradigm for machine learning and data science. In this work, we propose commutative algebra machine learning (CAML) for the prediction of protein−ligand binding affinities. Specifically, we apply persistent Stanley−Reisner theory, a key concept in combinatorial commutative algebra, to the affinity predictions of protein−ligand binding and metalloprotein−ligand binding. We present three new algorithms, i.e., element-specific commutative algebra, category-specific commutative algebra, and commutative algebra on bipartite complexes, to tackle the complexity of data involved in (metallo) protein−ligand complexes. We show that the proposed CAML outperforms other state-of-theart methods in (metallo) protein−ligand binding affinity predictions, indicating the great potential of commutative algebra learning.
Commutative Algebra Modeling in Materials Science – A Case Study on Metal–Organic Frameworks (MOFs)
Metal-organic frameworks (MOFs) are a class of important crystalline and highly porous materials whose hierarchical geometry and chemistry hinder interpretable predictions in materials properties. Commutative algebra is a branch of abstract algebra that has been rarely applied in data and material sciences. We introduce the first ever commutative algebra modeling and prediction in materials science. Specifically, category-specific commutative algebra (CSCA) is proposed as a new framework for MOF representation and learning. It integrates element-based categorization with multiscale algebraic invariants to encode both local coordination motifs and global network organization of MOFs. These algebraically consistent, chemically aware representations enable compact, interpretable, and data efficient modeling of MOF properties such as Henry’s constants and uptake capacities for common gases. Compared to traditional geometric and graph-based approaches, CSCA achieves comparable or superior predictive accuracy while substantially improving interpretability and stability across data sets. By aligning commutative algebra with the chemical hierarchy, the CSCA establishes a rigorous and generalizable paradigm for understanding structure and property relationships in porous materials and provides a nonlinear algebra-based framework for data-driven material discovery.
Reconciling Work Functions and Adsorption Enthalpies for Implicit Solvent Models: A Pt (111)/Water Interface Case Study
Implicit solvent models are a computationally efficient method of representing solid/liquid interfaces prevalent in electrocatalysis, energy storage, and materials science. However, electronic structure changes induced at the metallic surface by the dielectric continuum are not fully understood. To address this, we perform DFT calculations for the Pt(111)/water interface, in order to compare Poisson–Boltzmann continuum solvation methods with ab initio molecular dynamics (AIMD) simulations of explicit solvent. We show that the implicit solvent cavity can be parametrized in terms of the electric dipole moment change at the equilibrated explicit Pt/water interface to obtain the potential of zero charge (PZC). We also compare the accuracy of aqueous enthalpies of adsorption of phenol on Pt(111) using geometry and charge density based dielectric cavitation methods. The ability to parametrize the cavity according to individual atoms, as afforded in the geometry based approach, is key to obtaining accurate enthalpy changes of adsorption under aqueous conditions. Additionally, we show that the electronic structure changes induced by explicit solvent and our proposed implicit solvent parametrization scheme yield comparable density difference profiles and d-band projected density of states. We therefore demonstrate the capability of implicit solvent approaches to capture both the energetics of adsorption processes and the main electronic effects of aqueous solvent on the metallic surface. Therefore, this work provides a scheme for computationally efficient simulations of interfacial processes for applications in areas such as heterogeneous catalysis and electrochemistry.
Correction to Reconciling Work Functions and Adsorption Enthalpies for Implicit Solvent Models: A Pt (111)/Water Interface Case Study
This errata is to correct the acknowledgment in the original published article. G.B. (partial support), V.-A.G., M.-T.N., and R.R. were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division. Computer resources were provided by Research Computing at Pacific Northwest National Laboratory and the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. PNNL is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. G.B. acknowledges the EPSRC for partial support in PhD funding. The authors acknowledge the use of the IRIDIS High Performance Computing Facility (IRIDIS 5) and associated support services at the University of Southampton in the completion of this work. We are grateful to the UK Materials and Molecular Modeling Hub (Thomas HPC) for computational resources, which is partially funded by EPSRC (EP/P020194/1).
DMRG on Top of Plane-Wave Kohn–Sham Orbitals: A Case Study of Defected Boron Nitride
In this paper, we analyze the numerical aspects of the inherent multi reference density matrix renormalization group (DMRG) calculations on top of the periodic Kohn-Sham density functional theory using the complete active space approach. The potential of the framework is illustrated by studying hexagonal boron nitride nanoflakes embedding a charged single boron vacancy point defect by revealing a vertical energy spectrum with a prominent multireference character. We investigate the consistency of the DMRG energy spectrum from the perspective of sample size, basis size, and active space selection protocol. Results obtained from standard quantum chemical atom-centered basis calculations and plane-wave based counterparts show excellent agreement. Furthermore, we also discuss the spectrum of the periodic sheet which is in good agreement with extrapolated data of finite clusters. These results pave the way toward applying the DMRG method in extended correlated solid-state systems, such as point defect qubit in wide band gap semiconductors.
Data-Driven Many-Body Models for Molecular Fluids: CO 2 /H 2 O Mixtures as a Case Study
In this study, we extend the scope of the many-body TTM-nrg and MB-nrg potential energy functions (PEFs), originally introduced for halide ion–water and alkali-metal ion–water interactions, to the modeling of carbon dioxide (CO2) and water (H2O) mixtures as prototypical examples of molecular fluids. Both TTM-nrg and MB-nrg PEFs are derived entirely from electronic structure data obtained at the coupled cluster level of theory and are, by construction, compatible with MB-pol, a many-body PEF that has been shown to accurately reproduce the properties of water. Although both TTM-nrg and MB-nrg PEFs adopt the same functional forms for describing permanent electrostatics, polarization, and dispersion, they differ in the representation of short-range contributions, with the TTM-nrg PEFs relying on conventional Born–Mayer expressions and the MB-nrg PEFs employing multidimensional permutationally invariant polynomials. By providing a physically correct description of many-body effects at both short and long ranges, the MB-nrg PEFs are shown to quantitatively represent the global potential energy surfaces of the CO 2 –CO 2 and CO 2 –H 2 O dimers and the energetics of small clusters, as well as to correctly reproduce various properties in both gas and liquid phases. Furthermore, building upon previous studies of aqueous systems, our analysis provides further evidence for the accuracy and efficiency of the MB-nrg framework in representing molecular interactions in fluid mixtures at different temperature and pressure conditions.
From Molecules to Solids: A vdW-DF-C09 Case Study of the Mercury Dihalides
The mercury dihalides show a remarkable diversity in the structural preferences in their minimum energy structure types, spanning molecular to strongly bound ionic solids. A challenge in the development of density functional methods for extended systems is to arrive at strategies that serve equally well such a broad range of bonding modes or structural preferences. The chemical bonding and the stabilities of mercury dihalides and the general utility and reliability of the van der Waals density functional with C09 exchange (vdW-DF-C09) in predicting or describing the energetics and structural preferences in these metal dihalides is examined. Here, we show that, in contrast with the uncorrected generalized gradient approximation of the Perdew-Burke-Erzenhoff (PBE) exchange-correlation functional, qualitative and quantitative patterns in the bonding of the mercury dihalide solids are well reproduced with vdW-DF-C09 for the full series of HgX 2 systems for X = F, Cl, Br, and I. The possible existence of a low-temperature cotunnite polymorph for HgF 2 and PbF 2 is posited.
Density-Functional Tight-Binding Parameters for Bulk Zirconium: A Case Study for Repulsive Potentials
Density-functional tight-binding (DFTB) parameters are presented for the simulation of the bulk phases of zirconium. Electronic parameters were obtained using a band structure fitting strategy, while two-center repulsive potentials were created by particle swarm optimization. As objective functions for the repulsive potential fitting, we employed the Birch–Murnaghan equations of state for hexagonal close-packed (HCP), body-centered cubic (BCC) and ω phases of Zr from density-functional theory (DFT). When fractional atomic coordinates are not allowed to change in the generation of the equation-of-state curves, long-range repulsive DFTB potentials are able to almost perfectly reproduce equilibrium structures, relative DFT energies of the bulk phases, and bulk moduli. However, the same potentials lead to artifacts in the DFTB potential energy surfaces when atom positions in the unit cell are allowed to fully relax during the change of unit cell parameters. Finally, conventional short-range repulsive DFTB potentials, while inferior in their ability to reproduce DFT bulk energetics, are able to correctly reproduce the qualitative shape of the DFT potential energy surfaces, including the location of global minima, and can therefore be considered more transferable.
Measuring Electronic Structure of Multiply Charged Anions to Understand their Chemistry: A Case Study on Gaseous Polyhedral closo-Borate Dianions
Research on multiply charged anions (MCAs) in the gas phase has been intensively performed during the last decades, mainly to understand fundamental molecular physics phenomena, e.g., intramolecular Coulomb repulsion and existence of the repulsive Coulomb barrier. However, the relevance of these investigations with respect to understanding MCAs’ chemistry appears often vague. Here, we discuss how insights on the electronic structure obtained from negative ion photoelectron spectroscopy (NIPES) combined with theoretical calculations and collision induced dissociation can provide fundamental understanding on the intrinsic chemical reactivity of MCAs and their fragments. This is exemplified on our studies on polyhedral closo-borate dianions [BnXn]2- (n = 6, 10, 11, 12; X = H, F-I, CN) and their fragment ions. For example, the rational design of closo-borate dianions with specific electronic properties is described, which leads to generating highly reactive fragments. Depending on the dianionic precursor, these fragments are either tuned to bind noble gases effectively or to activate small molecules like CO and N2. The intrinsic electronic properties of closo-borate dianions are further compared to their electrochemistry in solutions, revealing solvent effects on the redox potentials. Neutral host molecules such as cyclodextrins are found to bind strongly to [BnXn]2-, and gas phase NIPES provides insights on the intrinsic host-guest interactions. Finally, outlooks including the direct NIPES of molecular fragment ions which cannot be generated in the condensed phase and their utilization in preparative mass spectrometry are discussed. J.W is grateful to the Volkswagen foundation for a Freigeist Fellowship. X. B. W acknowledges support from the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, the Division of Chemical Sciences, Geosciences and Biosciences. We are grateful to our colleagues who support our work on gas phase ion chemistry for many years. In particular we acknowledge the members of our groups, the Asmis group (Leipzig), Laskin Group (West Lafayette), the Jenne group (Wuppertal), the Finze group (Würzburg), the Grabowsky group (Bern), and the Sun group (Shanghai). We are grateful to Edoardo Apra for the many theoretical investigations on closo-borate anions. JW acknowledges support of Harald Knorke and Markus Rohdenburg with the preparation of graphical material, and XBW thanks Qinqin Yuan for the help in organizing references.
On the Network Topology of Cross-Linked Acrylate Photopolymers: A Molecular Dynamics Case Study
A reactive molecular dynamics approach is used to simulate cross-linking of acrylate polymer networks. By employing the same force field and reactive scheme and studying three representative multifunctional acrylate monomers, we isolate the importance of the nonreactive moieties within these model monomers. Analyses of reactive trajectories benchmark the estimated gel points, cyclomatic character, and spatially resolved cross-linking tendencies of the acrylates as a function of conversion. The insights into the similarities and differences of the polymerization and resulting networks presented here suggest molecular mechanics as a useful tool in the rational design of photopolymerization resins.
The Glycine N -Methyltransferase Case Study: Another Challenge for QM-Cluster Models?
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Kinetic Control of High-Pressure Phase Transition: A Case Study on [gamma] p-Nitrophenol
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Assigning Optical Absorption Transitions with Light-Induced Crystal Structures: Case Study of a Single-Crystal Nanooptomechanical Transducer
UV/vis absorption spectroscopy affords indirect structural information about the photochemistry and photophysics of molecules by inferring types of electronic transitions from spectral features. Direct structural information would become available, though, if light-induced crystal structures could be mapped against changes in optical absorption spectra as a photochemical process evolves. We present a series of light-induced crystal structures that track real-time changes in solid-state optical absorption spectra of a crystalline nanooptomechanical transducer, while the transduction process unfolds within its crystal lattice at 100 K. Results afford a combined structural and spectral mapping of its solid-state optical absorption, from which the operational mechanism of nanooptomechanical transduction is revealed. Metal-to-ligand and metal-centered charge-transfer bands are assigned to optical absorption peaks directly from their 3-D light-induced crystal structures. This approach could be used to characterize many solid-state optoelectronic materials.